Theoretical investigations concerning possible calcium sulfate, CaSO4, high-pressure polymorphs have been carried out. Total-energy calculations and geometry optimizations have been performed by using density functional theory at the B3LYP level for all crystal structures considered. The following sequence of pressure-driven structural transitions has been found: anhydrite, Cmcm (in parentheses the transition pressure) -> monazite-type, P2(1)/n (5 GPa) -> barite-type, Prima (8 GPa), and scheelite-type, I4(1)/a (8 GPa). The equation of state of the different polymorphs is determined, while their corresponding vibrational properties have been calculated and compared with previous theoretical results and experimental data.